| Min(phi) over symmetries of the knot is: [-2,-2,0,1,1,2,-1,0,1,2,3,0,0,2,2,0,1,0,0,0,1] |
| Flat knots (up to 7 crossings) with same phi are :['6.1269'] |
| Arrow polynomial of the knot is: -6*K1**2 - 4*K1*K2 + 2*K1 + 3*K2 + 2*K3 + 4 |
| Flat knots (up to 7 crossings) with same arrow polynomial are :['6.239', '6.428', '6.470', '6.556', '6.700', '6.910', '6.962', '6.1006', '6.1013', '6.1038', '6.1207', '6.1224', '6.1225', '6.1269', '6.1270', '6.1308', '6.1319', '6.1320', '6.1323', '6.1485', '6.1551', '6.1579', '6.1581', '6.1660', '6.1672', '6.1679', '6.1711', '6.1719', '6.1732', '6.1745', '6.1748', '6.1827', '6.1836', '6.1838', '6.1850', '6.1866'] |
| Outer characteristic polynomial of the knot is: t^7+49t^5+47t^3+8t |
| Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['6.1269'] |
| 2-strand cable arrow polynomial of the knot is: -192*K1**4*K2**2 + 480*K1**4*K2 - 3344*K1**4 + 352*K1**3*K2*K3 + 32*K1**3*K3*K4 - 480*K1**3*K3 + 384*K1**2*K2**3 - 5856*K1**2*K2**2 - 992*K1**2*K2*K4 + 10592*K1**2*K2 - 464*K1**2*K3**2 - 128*K1**2*K4**2 - 6908*K1**2 + 96*K1*K2**3*K3 - 608*K1*K2**2*K3 - 96*K1*K2**2*K5 - 64*K1*K2*K3*K4 + 7888*K1*K2*K3 + 1776*K1*K3*K4 + 192*K1*K4*K5 - 792*K2**4 - 240*K2**2*K3**2 - 16*K2**2*K4**2 + 1440*K2**2*K4 - 5396*K2**2 + 352*K2*K3*K5 + 32*K2*K4*K6 - 2616*K3**2 - 998*K4**2 - 156*K5**2 - 12*K6**2 + 5740 |
| Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['6.1269'] |
| Virtual knots (up to 6 crossings) projecting to this knot are :'vk6.16501', 'vk6.16594', 'vk6.18098', 'vk6.18436', 'vk6.22928', 'vk6.23025', 'vk6.24545', 'vk6.24964', 'vk6.34909', 'vk6.35018', 'vk6.36680', 'vk6.37104', 'vk6.42474', 'vk6.42587', 'vk6.43956', 'vk6.44273', 'vk6.54728', 'vk6.54825', 'vk6.55922', 'vk6.56216', 'vk6.59188', 'vk6.59253', 'vk6.60448', 'vk6.60811', 'vk6.64748', 'vk6.64807', 'vk6.65564', 'vk6.65876', 'vk6.68040', 'vk6.68105', 'vk6.68642', 'vk6.68857'] |
| The R3 orbit of minmal crossing diagrams contains: |
| The diagrammatic symmetry type of this knot is c. |
| The reverse -K is |
| The mirror image K* is |
| The reversed mirror image -K* is |
| The fillings (up to the first 10) associated to the algebraic genus: |
| Or click here to check the fillings |
| invariant | value |
|---|---|
| Gauss code | O1O2O3U1O4O5U2U5O6U3U4U6 |
| R3 orbit | {'O1O2O3U1O4O5U2U5O6U3U4U6'} |
| R3 orbit length | 1 |
| Gauss code of -K | O1O2O3U4U5U1O4U6U2O6O5U3 |
| Gauss code of K* | O1O2O3U4U5U1O4U2U6O5O6U3 |
| Gauss code of -K* | O1O2O3U1O4O5U4U2O6U3U5U6 |
| Diagrammatic symmetry type | c |
| Flat genus of the diagram | 3 |
| If K is checkerboard colorable | False |
| If K is almost classical | False |
| Based matrix from Gauss code | [[ 0 -2 -2 0 1 1 2],[ 2 0 1 2 2 1 1],[ 2 -1 0 2 3 1 2],[ 0 -2 -2 0 1 0 2],[-1 -2 -3 -1 0 0 1],[-1 -1 -1 0 0 0 0],[-2 -1 -2 -2 -1 0 0]] |
| Primitive based matrix | [[ 0 2 1 1 0 -2 -2],[-2 0 0 -1 -2 -1 -2],[-1 0 0 0 0 -1 -1],[-1 1 0 0 -1 -2 -3],[ 0 2 0 1 0 -2 -2],[ 2 1 1 2 2 0 1],[ 2 2 1 3 2 -1 0]] |
| If based matrix primitive | True |
| Phi of primitive based matrix | [-2,-1,-1,0,2,2,0,1,2,1,2,0,0,1,1,1,2,3,2,2,-1] |
| Phi over symmetry | [-2,-2,0,1,1,2,-1,0,1,2,3,0,0,2,2,0,1,0,0,0,1] |
| Phi of -K | [-2,-2,0,1,1,2,-1,0,1,2,3,0,0,2,2,0,1,0,0,0,1] |
| Phi of K* | [-2,-1,-1,0,2,2,0,1,0,2,3,0,0,0,1,1,2,2,0,0,-1] |
| Phi of -K* | [-2,-2,0,1,1,2,-1,2,1,3,2,2,1,2,1,0,1,2,0,0,1] |
| Symmetry type of based matrix | c |
| u-polynomial | t^2-2t |
| Normalized Jones-Krushkal polynomial | 3z^2+24z+37 |
| Enhanced Jones-Krushkal polynomial | 3w^3z^2+24w^2z+37w |
| Inner characteristic polynomial | t^6+35t^4+20t^2+1 |
| Outer characteristic polynomial | t^7+49t^5+47t^3+8t |
| Flat arrow polynomial | -6*K1**2 - 4*K1*K2 + 2*K1 + 3*K2 + 2*K3 + 4 |
| 2-strand cable arrow polynomial | -192*K1**4*K2**2 + 480*K1**4*K2 - 3344*K1**4 + 352*K1**3*K2*K3 + 32*K1**3*K3*K4 - 480*K1**3*K3 + 384*K1**2*K2**3 - 5856*K1**2*K2**2 - 992*K1**2*K2*K4 + 10592*K1**2*K2 - 464*K1**2*K3**2 - 128*K1**2*K4**2 - 6908*K1**2 + 96*K1*K2**3*K3 - 608*K1*K2**2*K3 - 96*K1*K2**2*K5 - 64*K1*K2*K3*K4 + 7888*K1*K2*K3 + 1776*K1*K3*K4 + 192*K1*K4*K5 - 792*K2**4 - 240*K2**2*K3**2 - 16*K2**2*K4**2 + 1440*K2**2*K4 - 5396*K2**2 + 352*K2*K3*K5 + 32*K2*K4*K6 - 2616*K3**2 - 998*K4**2 - 156*K5**2 - 12*K6**2 + 5740 |
| Genus of based matrix | 1 |
| Fillings of based matrix | [[{3, 6}, {4, 5}, {1, 2}], [{3, 6}, {4, 5}, {2}, {1}]] |
| If K is slice | False |